*What is your controller that you are using with Dolphin?
*What are you trying to do exactly?
*Post a screenshot of your GCpad config and paste the link here and/or attach it.

EDIT: Don't max out the post subject. MyBB insists on adding "RE: " to every reply, and if you max it out, there's no room left for us to reply with, and we have to edit the subject of our replies. It's dumb, but that's how it is, so please don't max it out.

*the below assumes you are using the SCP drivers to emulate a 360 controller*

You need to assign L-analog and R-analog. GC games always expect analog before digital because of how their triggers are designed, skipping to digital can freak a lot of games out. The 90 threshold will allow you to assign them both to L2 and R2, with a soft press for analog and full press for digital similar to a gamecube controller, and it should allow you to small shield and things in melee. And that threshold of 1 could be an issue, digital buttons don't need the threshold, so I suggest just going with the default of 50 on them. Other than that, your settings look good.

*Small shield in melee
*Accelerating in racing games
*running while spraying in sunshine
*sidestepping in metroid prime 1/2
*accelerating in rogue leader and rebel strike

And that's just off the top of my head. You said your goal was to 100% emulate the GameCube controller, no? Well a ton of games use the analog and digital functions in tandem, as that is how the GameCube controller was designed.

The small shield is a different type of shield in melee that is only available with an analog (not digital) press. There are a number of advanced strategies that use the small shield instead of the full shield.

Small shielding is the wrong term for it though. The resulting shield is actually larger than the shield you get from a digital press! But the larger shield is lighter in color, since the implication is that it's as if you took the normal shield and spread it in a thinner yet wider circle around yourself. Hence, light shielding.